1. Bohr Model of the Atom
College Chemistry

2. Atomic Spectra
Atoms of different elements emit light at specific wavelengths
Emission spectrum or line spectra
Line spectra can be seen by looking at light through a prism called a spectroscope
Spectra of solids are usually a continuous band of colors, spectra of gases are a series of sharp lines
Ex: yellow color in street lights given off by sodium

3. Atomic Spectra Each line emitted corresponds to a specific color
You can differentiate between different atoms based on their atomic spectra
Spectroscopy can also be used to detect the motion or position of stars
Stars give off hydrogen
Early astronomers looked for the wavelengths of H (615 and 651 nm) in the night sky

4. Absorption Spectrum
“cool” atoms that do not emit light will absorb light at different, characteristic wavelengths
Absorption spectrum
To obtain a spectrum, white light is shined through a sample of gas then a spectroscope
The normally white light will then have dark light lines on it
Most gases absorb and emit light at the same wavelengths
Can use absorption spectrum to determine the identity of an element

5. Bohr Model of the Atom
How come elements can emit its own characteristic wavelengths?
Remember – Planck said energy of electrons are quantized
Bohr started with hydrogen – the simplest atom
Labeled each energy level (and each orbit) by a number – quantum number, n
Lowest energy (ground state) = 1
Energy level closest to the nucleus

6. Bohr Model of the Atom
When an electron absorbs energy, it “jumps” to the next orbital further away from the nucleus – excited states
Excited states: n = 2, n = 3, n = etc

7. Bohr Model of the Atom
Bohr proposed that when radiation (energy) is absorbed, an electron jumps from the ground state to the excited state
Radiation (light) is emitted when the electron falls from the higher energy to the lower energy

8. Bohr Model of the Atom
Bohr showed that the energies that the electron in hydrogen can possess are given by
En = -Rh(1/n2)
E = energy (J) n = principal quantum #
R = Rydberg’s constant, 2.18 x J
Negative sign is arbitrary, just signifies that the energy of the electron in the atom is lower than the free electron

9. Bohr Model of the Atom
Ground state – n = 1, lowest energy state of a system (atom)
Excited state – n = 2,3, etc, higher than the ground state, orbitals furthest from ground state

10. Bohr Model of the Atom
We can apply the Bohr equation to determine the amount of energy left when electrons are emitted from a photon
DE = hv = Rh(1 – 1)
ni2 nf2
When a photon is emitted, ni > nf, so DE will be negative, this does NOT mean energy is energy, you can never have negative energy

11. Example 7.4
What is the wavelength of a photon (in nm) emitted during a transition from the ni = 5 to the nf = 2 state in the hydrogen atom?
DE = hv = Rh(1 – 1)
ni2 nf2
DE = 2.18 x J(1/52 – 1/22)
= x J, negative, so emission
l = c/v or, rearranged, l = ch/DE
l = (3.00 x 108 m/s)(6.63 x J*s)
4.58 x J
l – 4.34 x 10-7 m (divide by 1 x 10-9 m) = 434 nm

12. Louis de Broglie
We have mentioned light can act as both waves and particles
de Broglie determined matter too can act as both waves and particles
Why do we not feel the “wave”?
Particles must be very small (smaller than we can see) in order to have a wavelength large enough for us to see

13. Louis de Broglie
According to de Broglie, an electron bound to the nucleus behaves like a standing wave
He then argued that the length of the wave must fit the circumference of the orbit
His reasoning (and math) lead to the conclusion that waves can behave like particles and particles can exhibit wavelike properties
l = h/mu m = mass (kg) u = velocity (m/s)

14. Example 7.5
Calculate the wavelength of the “particle” in the following case: (a) The fastest serve in tennis is about 140 mph, or 63 m/s. Calculate the wavelength associated with a 6.0 x 10-2 kg tennis ball traveling at this speed.
l = h/mu
l = (6.36 x J*s) /( 6.0 x 10-2 kg * 63 m/s)
l = 1.8 x m, so small that we cannot detect the “wave” particles of a tennis ball

15. What is YOUR wavelength?
l = h/mu
Pound to kilogram conversion: 1 lb = 0.45 kg